Accounting for clock boundaries in approximation error
An exact-arithmetic component now encloses the endpoint-average error when derivative bounds and boundary-jump bounds are supplied. It does not silently treat missing jump information as zero. Unsupported jumps in the residual itself are rejected.
Fourteen focused checks cover smooth examples, derivative steps and hinges, an independently integrated piecewise quadratic, outward endpoints and incomplete or invalid bounds. The result keeps native clock coverage and native derivative bounds explicitly unverified.
This supplies one mathematical part of the next prediction bound. The native calculation must still provide valid derivative and jump bounds over its whole declared parameter/clock region. No new integration or aircraft fit was run.